Three different products get called "online calendar software", and choosing badly here wastes more time than any other decision in this list. The first is a shared web calendar: fixtures, room bookings, an events diary that a group of people read in a browser. The second is a personal calendar server that syncs both ways with the calendar app on your phone and laptop, which is the CalDAV protocol and means Baikal, Radicale, DAViCal or Nextcloud. The third is appointment booking, where somebody picks a slot from your availability, which is Calendly (priced per seat per month, with a free tier limited to one event type), Doodle, or Google Calendar's own appointment schedules.
WebCalendar, the application in this category, is firmly the first of those three. It is a multi-user web calendar with groups, categories, resource booking, event approval before publication, iCalendar import and export, and public calendars people can subscribe to as a feed. It has been going since the early 2000s, and the assumption that it therefore died somewhere around 2013 is wrong: version 1.9.23 was released on 12 August 2026, following eight releases since February of the same year, and it requires PHP 8.2 or newer.
What it does not do is two-way sync. Your phone can subscribe to a WebCalendar feed and read it. Your phone cannot edit an event and have the change appear on the server. If that is what you need, you want a CalDAV server, and the good news is that Baikal is also PHP and also runs on ordinary hosting.